{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<small><i>This notebook was put together by [Jake Vanderplas](http://www.vanderplas.com). Source and license info is on [GitHub](https://github.com/jakevdp/sklearn_tutorial/).</i></small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supervised Learning In-Depth: Random Forests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Previously we saw a powerful discriminative classifier, **Support Vector Machines**.\n",
    "Here we'll take a look at motivating another powerful algorithm. This one is a *non-parametric* algorithm called **Random Forests**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "plt.style.use('seaborn')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivating Random Forests: Decision Trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random forests are an example of an *ensemble learner* built on decision trees.\n",
    "For this reason we'll start by discussing decision trees themselves.\n",
    "\n",
    "Decision trees are extremely intuitive ways to classify or label objects: you simply ask a series of questions designed to zero-in on the classification:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nZ2cUFRVh9uzZYt/XuLg4/PrrrwAADw8PyMvLV/lYimL+/PlzuX0B5eTkuPcz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\nx3Ecx3USL5w4juM4juM66f8AUqSfVyNHMk8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import fig_code\n",
    "fig_code.plot_example_decision_tree()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The binary splitting makes this extremely efficient.\n",
    "As always, though, the trick is to *ask the right questions*.\n",
    "This is where the algorithmic process comes in: in training a decision tree classifier, the algorithm looks at the features and decides which questions (or \"splits\") contain the most information.\n",
    "\n",
    "### Creating a Decision Tree\n",
    "\n",
    "Here's an example of a decision tree classifier in scikit-learn. We'll start by defining some two-dimensional labeled data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Ht1/hent0SOCF4GIr17j3IcooL1H0bt0p+M9jGPXqF21r1JiCJ0ZhnH5G3I9v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\nOaJq93F8YAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "X, y = make_blobs(n_samples=300, centers=4,\n",
    "                  random_state=0, cluster_std=1.0)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='rainbow');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have some convenience functions in the repository that help "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from fig_code import visualize_tree, plot_tree_interactive"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now using IPython's ``interact`` (available in IPython 2.0+, and requires a live kernel) we can view the decision tree splits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6cc005f7ad78431fbf0e3cb47887af57",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_tree_interactive(X, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that at each increase in depth, every node is split in two **except** those nodes which contain only a single class.\n",
    "The result is a very fast **non-parametric** classification, and can be extremely useful in practice.\n",
    "\n",
    "**Question: Do you see any problems with this?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Decision Trees and over-fitting\n",
    "\n",
    "One issue with decision trees is that it is very easy to create trees which **over-fit** the data. That is, they are flexible enough that they can learn the structure of the noise in the data rather than the signal! For example, take a look at two trees built on two subsets of this dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 576x396 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mfZsg27ZGKzUrjuKMF47R9hUnc5sO1I57hfQYqiDEUOdGi8WLZe1bD/Pm5c+u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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 576x396 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Dvh7Y+bPYABvF+V2w9X/B+YXC+6g4Si6eMJx82h9RLvb5pORe/AALEArB1q3w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\nEfH/A3bAb8arcvdyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeClassifier\n",
    "clf = DecisionTreeClassifier()\n",
    "\n",
    "plt.figure()\n",
    "visualize_tree(clf, X[:200], y[:200], boundaries=False)\n",
    "plt.figure()\n",
    "visualize_tree(clf, X[-200:], y[-200:], boundaries=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The details of the classifications are completely different! That is an indication of **over-fitting**: when you predict the value for a new point, the result is more reflective of the noise in the model rather than the signal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ensembles of Estimators: Random Forests\n",
    "\n",
    "One possible way to address over-fitting is to use an **Ensemble Method**: this is a meta-estimator which essentially averages the results of many individual estimators which over-fit the data. Somewhat surprisingly, the resulting estimates are much more robust and accurate than the individual estimates which make them up!\n",
    "\n",
    "One of the most common ensemble methods is the **Random Forest**, in which the ensemble is made up of many decision trees which are in some way perturbed.\n",
    "\n",
    "There are volumes of theory and precedent about how to randomize these trees, but as an example, let's imagine an ensemble of estimators fit on subsets of the data. We can get an idea of what these might look like as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c4b3ba815b41440db4c8b743967ff158",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def fit_randomized_tree(random_state=0):\n",
    "    X, y = make_blobs(n_samples=300, centers=4,\n",
    "                      random_state=0, cluster_std=2.0)\n",
    "    clf = DecisionTreeClassifier(max_depth=15)\n",
    "    \n",
    "    rng = np.random.RandomState(random_state)\n",
    "    i = np.arange(len(y))\n",
    "    rng.shuffle(i)\n",
    "    visualize_tree(clf, X[i[:250]], y[i[:250]], boundaries=False,\n",
    "                   xlim=(X[:, 0].min(), X[:, 0].max()),\n",
    "                   ylim=(X[:, 1].min(), X[:, 1].max()))\n",
    "    \n",
    "from ipywidgets import interact\n",
    "interact(fit_randomized_tree, random_state=(0, 100));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See how the details of the model change as a function of the sample, while the larger characteristics remain the same!\n",
    "The random forest classifier will do something similar to this, but use a combined version of all these trees to arrive at a final answer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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B6kfkvPOOcnuRiKYmaf/xfD6lpWybAEWwD9XW5z4H/Pa3yntZsQK44IL4jJlzRp6TbPuc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\nS0REFKH/A8szVjBp5JL0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "clf = RandomForestClassifier(n_estimators=100, random_state=0)\n",
    "visualize_tree(clf, X, y, boundaries=False);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By averaging over 100 randomly perturbed models, we end up with an overall model which is a much better fit to our data!\n",
    "\n",
    "*(Note: above we randomized the model through sub-sampling... Random Forests use more sophisticated means of randomization, which you can read about in, e.g. the [scikit-learn documentation](http://scikit-learn.org/stable/modules/ensemble.html#forest)*)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quick Example: Moving to Regression\n",
    "\n",
    "Above we were considering random forests within the context of classification.\n",
    "Random forests can also be made to work in the case of regression (that is, continuous rather than categorical variables). The estimator to use for this is ``sklearn.ensemble.RandomForestRegressor``.\n",
    "\n",
    "Let's quickly demonstrate how this can be used:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jKCRfAEZF9ai+MHNLUm5TALbo7GibsltXsiqhxno7RlFIvgAQcblJKrul5H/d\nucyX58+tpDZZbdzZ0TZlFKW2pvQDfHLj33ewrwKRTkXyBRCoreuXaufGfws6jMibnKQ237LYt97h\naCo9rZJ6+55DViz3kfJXgm99+kDF4yf5AoAPgi4+Cortm6YEtVyJ5AsA8Mz2TVOCWq5E8gUAeBaW\nTVNGU2lP885BLVci+QIA8urp7VfGkTKOXBNaGDZNyR7W4WXeOajlSiRfAMA02UKkLLeEVluTzFtJ\nbXK5Tznzzvkqwbv+/fKKx0/yBQBMU0ohUqUqqYtV7rxzbvxXLmr3M7y87F5hDcBabLQRbjbtm5ys\nSuRNwGHeZpKeLwBgmpkKkcJ0RGEY5p1LRfIFAExTqBApbEcU5h7WEcS8c6kYdgaAmPBrqD9sRxRm\nX1d2k5PNtywOJI5S0PMFAExTqOCqUkcUxgnJFwAwTaGCq3KOKMQ4ki8AlCnIU30qpVDBVVSPKDSJ\n5AsAZchXfGTTqT5uChVc5duYorG+xtNxfnFF8gWAMgR1Kk6lZRNsVm4Fce7GFCTe0jBGAABlsGkz\nilJ1drRpx6/Gt5icqYKYTVNKQ/IFgDLMm9ugvoHpiTbMuythOtM3Dww7A0AZgjoVB3aj5wsAZcjO\ngT7+Yq/SGUftrY0TRUmAG5IvAJSps6NNz796WJIduytFlU3zziRfAICrlqa6oEOIJOZ8AQAwjOQL\nAIBhJF8AAAxjzhcA4IkNBU7ZYwbDFivJFwDgKmxJKyoYdgYAwDCSLwAAhpF8AQAwjOQLAD7Yun4p\n86MhNTg0MlF4FRaeCq6GhobU1dWl4eFhpVIp3XPPPVq0aJHfsQEAEEmeku8TTzyhL3zhC1q3bp3+\n/ve/a8OGDfr5z3/ud2wAAESSp+S7bt06zZo1S5KUTqdVW1vra1AAAETZjMl39+7devLJJ6dc27Jl\niy655BINDAyoq6tL995774y/qKWlQdXVSe+Rfqy1tans58A42tIftKM/aEd/0I5TJZMJKZFQMpko\nqW0q3Y4zJt9Vq1Zp1apV066//fbb+va3v63vfOc7Wrx45iO0BgdPeYtwktbWJg0MDJX9PKAt/UI7\n+oN29AftOF067UiOo3TaKbpt/GrHQgncU7Xz3/72N91555165JFHdNVVV3kODACASunp7deHw6PK\nONKHw6Pq6e0POqQJnuZ8H3nkEZ05c0Y/+MEPJEmNjY167LHHfA0MAACvenr7tX3PoYnH6Ywz8biz\noy2osCZ4Sr4kWgBAmL30+jsu14+EIvmyyQYAIHKOvp+/zujY8ZOGI8mP5AsAiJx5cxvyXj//vNmG\nI8mP5AsAiJwVSxbkvf65+c3d1MqUAAAG4klEQVRmA3FB8gUARE5nR5uuubx92vVXDvSFouqZ5AsA\niKS33x3Me/2l148YjmQ6ki8AIJLCXHRF8gUARFKYi65IvgCASHIrulqx5AKzgeRB8gUARFJnR5sa\n62smHre3NurWGy4OxSYbnna4AgDABrU1SZ0aSamlqU6bb5n5ECBT6PkCAGAYyRcAMEVX9351de8P\nOoxII/kCAGAYyRcAAMNIvgAAGEbyBQBE1tb1S9XSVBd0GNOQfAEAMIzkCwCAYSRfAAAMI/kCAGAY\n20sCACJt6/qlQYcwDT1fAAAMI/kCAGAYyRcAMKGnt18fDo/q+IkRbdrZo57e/qBDiiTmfAEAksYT\n7/Y9hyYe9w2cnHgchjNwo4SeLwBAkvTS6++4XD9iNI44IPkCACRJR98/lff6seMnDUcSfSRfAIAk\nad7chrzXzz9vtuFIoo/kCwCQJK1YssDl+gVmA4kBCq4AAJLOFlU9/mKv0hlH7a2NWrHkAoqtKoDk\nCwCY0NnRpudfPSxJ2nzL4oCjiS6GnQEAMIzkCwCAYSRfAAAMI/kCAGAYyRcAAMNIvgAAGEbyBQDA\nMJIvAACGkXwBADCMHa4AAFNsXb806BAiz1PyPXXqlDZs2KCPPvpI9fX12rp1q84991y/YwMAIJI8\nDTs/99xzuvjii7Vr1y6tWLFC3d3dfscFAEBkeer5rlu3Tul0WpJ09OhRzZ0719egAACIsoTjOE6h\nH9i9e7eefPLJKde2bNmiSy65RDfddJP+8pe/6IknntDChQsL/qKxsbSqq5PlRwwAgOVmTL4zOXz4\nsG699Vbt3bu34M8NDAyV82skSa2tTb48D2hLv9CO/qAd/UE7+sOvdmxtbXL9N09zvtu3b9cvfvEL\nSVJDQ4OSSXq0AAAUy9Oc79e//nXdfffdeuGFF5ROp7Vlyxa/4wIAILI8Jd+5c+dq586dfscCAEAs\nsMMVAACGkXwBADCM5AsAgGEkXwAADCP5AgBgWNmbbAAAgNLQ8wUAwDCSLwAAhpF8AQAwjOQLAIBh\nJF8AAAwj+QIAYJgVyTeTyWjTpk268cYbtXbtWh05ciTokKyUSqXU1dWlNWvWaOXKlXrllVeCDslq\nx48f11VXXaXDhw8HHYq1tm/frhtvvFFf+9rXtHv37qDDsVIqldKGDRu0evVqrVmzhs+jB2+++abW\nrl0rSTpy5Ii+8Y1vaM2aNfr+97+vTCZTkd9pRfLdu3evzpw5o2effVYbNmzQQw89FHRIVtqzZ4+a\nm5u1a9cu7dixQ/fff3/QIVkrlUpp06ZNqqurCzoUa/X09OjgwYN65pln9NRTT+mf//xn0CFZ6be/\n/a3Gxsb005/+VLfffrv+8z//M+iQrLJjxw5t3LhRo6OjkqQHH3xQd911l3bt2iXHcSrWSbEi+R44\ncEDLli2TJF166aV66623Ao7ITtddd53uvPPOicfJZDLAaOz28MMPa/Xq1frEJz4RdCjWeu2113TR\nRRfp9ttv1ze/+U1dffXVQYdkpU996lNKp9PKZDIaHh5WdbWnk2Jja/78+Xr00UcnHh86dEiLFy+W\nJF155ZXav39/RX6vFe/S8PCwGhsbJx4nk0mNjY3xISvR7NmzJY235x133KG77ror4Ijs9LOf/Uzn\nnnuuli1bph/96EdBh2OtwcFBHT16VNu2bVNfX59uu+02/frXv1YikQg6NKs0NDTovffe05e+9CUN\nDg5q27ZtQYdkleXLl6uvr2/iseM4E5/B2bNna2hoqCK/14qeb2Njo06ePDnxOJPJkHg9OnbsmG66\n6SZ99atf1fXXXx90OFZ64YUXtH//fq1du1Z//vOfdffdd2tgYCDosKzT3NysK664QrNmzdKFF16o\n2tpaffDBB0GHZZ0f//jHuuKKK/Tyyy/rl7/8pe65556JIVSUrqrqbFo8efKk5syZU5nfU5Fn9dll\nl12mffv2SZLeeOMNXXTRRQFHZKf3339fN998s7q6urRy5cqgw7HWT37yEz399NN66qmntHDhQj38\n8MNqbW0NOizrXH755frd734nx3HU39+v06dPq7m5OeiwrDNnzhw1NTVJks455xyNjY0pnU4HHJW9\nOjo61NPTI0nat2+fPv/5z1fk91jRfbz22mv1+9//XqtXr5bjONqyZUvQIVlp27ZtOnHihLq7u9Xd\n3S1pvNiAoiEE4Ytf/KL+8Ic/aOXKlXIcR5s2baIOwYN169bp3nvv1Zo1a5RKpfStb31LDQ0NQYdl\nrbvvvlvf+9739MMf/lAXXnihli9fXpHfw6lGAAAYZsWwMwAAUULyBQDAMJIvAACGkXwBADCM5AsA\ngGEkXwAADCP5AgBgGMkXAADD/j+mcq7s3qUxmgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor\n",
    "\n",
    "x = 10 * np.random.rand(100)\n",
    "\n",
    "def model(x, sigma=0.3):\n",
    "    fast_oscillation = np.sin(5 * x)\n",
    "    slow_oscillation = np.sin(0.5 * x)\n",
    "    noise = sigma * np.random.randn(len(x))\n",
    "\n",
    "    return slow_oscillation + fast_oscillation + noise\n",
    "\n",
    "y = model(x)\n",
    "plt.errorbar(x, y, 0.3, fmt='o');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lqoivYRhEXn0FD6C4muZ9noLlu/7g1qL7R8YzbNkVnMzOr0LjisHBAQCcTR4a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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xfit = np.linspace(0, 10, 1000)\n",
    "yfit = RandomForestRegressor(100).fit(x[:, None], y).predict(xfit[:, None])\n",
    "ytrue = model(xfit, 0)\n",
    "\n",
    "plt.errorbar(x, y, 0.3, fmt='o')\n",
    "plt.plot(xfit, yfit, '-r');\n",
    "plt.plot(xfit, ytrue, '-k', alpha=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the non-parametric random forest model is flexible enough to fit the multi-period data, without us even specifying a multi-period model!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Random Forest for Classifying Digits\n",
    "\n",
    "We previously saw the **hand-written digits** data. Let's use that here to test the efficacy of the SVM and Random Forest classifiers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'target_names', 'images', 'DESCR'])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "digits.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1797, 64)\n",
      "(1797,)\n"
     ]
    }
   ],
   "source": [
    "X = digits.data\n",
    "y = digits.target\n",
    "print(X.shape)\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To remind us what we're looking at, we'll visualize the first few data points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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efvpp5OXl4aWXXkJPTw/y8/MRFRXldlm28Pt3KCtXrnSiDtctWbLE7RJsN2TI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\nHyWHNGzoDpsqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x432 with 64 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set up the figure\n",
    "fig = plt.figure(figsize=(6, 6))  # figure size in inches\n",
    "fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)\n",
    "\n",
    "# plot the digits: each image is 8x8 pixels\n",
    "for i in range(64):\n",
    "    ax = fig.add_subplot(8, 8, i + 1, xticks=[], yticks=[])\n",
    "    ax.imshow(digits.images[i], cmap=plt.cm.binary, interpolation='nearest')\n",
    "    \n",
    "    # label the image with the target value\n",
    "    ax.text(0, 7, str(digits.target[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can quickly classify the digits using a decision tree as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import metrics\n",
    "\n",
    "Xtrain, Xtest, ytrain, ytest = train_test_split(X, y, random_state=0)\n",
    "clf = DecisionTreeClassifier(max_depth=11)\n",
    "clf.fit(Xtrain, ytrain)\n",
    "ypred = clf.predict(Xtest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check the accuracy of this classifier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8288888888888889"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.accuracy_score(ypred, ytest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and for good measure, plot the confusion matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 576x396 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(metrics.confusion_matrix(ypred, ytest),\n",
    "           interpolation='nearest', cmap=plt.cm.binary)\n",
    "plt.grid(False)\n",
    "plt.colorbar()\n",
    "plt.xlabel(\"predicted label\")\n",
    "plt.ylabel(\"true label\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "1. Repeat this classification task with ``sklearn.ensemble.RandomForestClassifier``.  How does the ``max_depth``, ``max_features``, and ``n_estimators`` affect the results?\n",
    "2. Try this classification with ``sklearn.svm.SVC``, adjusting ``kernel``, ``C``, and ``gamma``. Which classifier performs optimally?\n",
    "3. Try a few sets of parameters for each model and check the F1 score (``sklearn.metrics.f1_score``) on your results. What's the best F1 score you can reach?"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
